On magnetic-field consistency in the sideways force calculation of Phys. Plasmas 27, 012508 (2020)
Abstract
We examine the consistency of the equilibrium magnetic field B0 used in the analytical calculation of the sideways wall force by A. A. Martynov and S. Yu. Medvedev [Phys. Plasmas 27, 012508 (2020)] and the subsequent reformulation presented in [Phys. Plasmas 27, 054702 (2020)]. In these attempts, the current density j0 = ∇ × B0 must vanish in the vacuum regions adjacent to the wall, making B0 curl-free as a complement to the natural ∇ · B0 = 0. Since the cited works incorporate selected toroidal corrections without explicitly specifying the corresponding differential operators, we test B0 adopted in these models against Maxwell's equations using both toroidal and quasi-cylindrical formulations. We show that the divergence-free requirement is violated in the toroidal interpretation, while the curl-free condition is not satisfied in the quasi-cylindrical limit. The reformulation likewise fails to define a self-consistent equilibrium field with toroidal effects because the accompanying field corrections required for consistency with Maxwell's equations are not specified. Since the sideways force calculations are built upon these inconsistent field prescriptions, their analytical derivations are consequently compromised. The resulting arguments therefore cannot serve as a valid basis for revising either the earlier results established by D. V. Mironov and V. D. Pustovitov [Phys. Plasmas 24, 092508 (2017)] or those obtained within the single-harmonic analysis [Phys. Plasmas 22, 052502 (2015)].
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BibTeX
@misc{mironov2026magneticfield,
title = {{On magnetic-field consistency in the sideways force calculation of Phys. Plasmas 27, 012508 (2020)}},
author = {Denis Mironov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20644},
eprint = {2610.20644},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20644},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - On magnetic-field consistency in the sideways force calculation of Phys. Plasmas 27, 012508 (2020)
AU - Denis Mironov
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.20644
UR - https://arxiv.org/abs/2610.20644
AB - We examine the consistency of the equilibrium magnetic field B_0 used in the analytical calculation of the sideways wall force by A. A. Martynov and S. Yu. Medvedev [Phys. Plasmas 27, 012508 (2020)] and the subsequent reformulation presented in [Phys. Plasmas 27, 054702 (2020)]. In these attempts, the current density j_0 = ∇ × B_0 must vanish in the vacuum regions adjacent to the wall, making B_0 curl-free as a complement to the natural ∇ · B_0 = 0. Since the cited works incorporate selected toroidal corrections without explicitly specifying the corresponding differential operators, we test B_0 adopted in these models against Maxwell's equations using both toroidal and quasi-cylindrical formulations. We show that the divergence-free requirement is violated in the toroidal interpretation, while the curl-free condition is not satisfied in the quasi-cylindrical limit. The reformulation likewise fails to define a self-consistent equilibrium field with toroidal effects because the accompanying field corrections required for consistency with Maxwell's equations are not specified. Since the sideways force calculations are built upon these inconsistent field prescriptions, their analytical derivations are consequently compromised. The resulting arguments therefore cannot serve as a valid basis for revising either the earlier results established by D. V. Mironov and V. D. Pustovitov [Phys. Plasmas 24, 092508 (2017)] or those obtained within the single-harmonic analysis [Phys. Plasmas 22, 052502 (2015)].
ER -